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apop_fexact.c
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apop_fexact.c
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/** \file apop_fexact.c
Fisher's exact test for contingency tables
This file primarily consists of an algorithm from the ACM, fully
documented below. The C code below was cut and pasted from the
R project. Thanks, guys.
Un-R-ifying modifications Copyright (c) 2006--2009 by Ben Klemens.
Licensed under the GPLv2; see COPYING.
R version credits:
fexact.f -- translated by f2c (version 19971204).\\
Run through a slightly modified version of MM's f2c-clean.\\
Heavily hand-edited by KH and MM.
*/
#include "apop_internal.h"
#include <gsl/gsl_sf.h>
#include <gsl/gsl_math.h>
#include <stdbool.h>
/* These are the R-specific items. */
typedef enum { FALSE = 0, TRUE /*, MAYBE */ } Rboolean;
int imax2(int a, int b){return (a>b) ? a : b;}
int imin2(int a, int b){return (a<b) ? a : b;}
float fmax2(float a, float b){return (a>b) ? a : b;}
float fmin2(float a, float b){return (a<b) ? a : b;}
/* end R-to-Apophenia additions */
static void f2xact(int nrow, int ncol, int *table, int ldtabl,
double *expect, double *percnt, double *emin,
double *prt, double *pre, double *fact, int *ico, int *iro,
int *kyy, int *idif, int *irn, int *key,
int *ldkey, int *ipoin, double *stp, int *ldstp,
int *ifrq, double *LP, double *SP, double *tm,
int *key2, int *iwk, double *rwk);
static double f3xact(int nrow, int *irow, int ncol, int *icol, int ntot,
double *fact, int *ico, int *iro,
int *it, int *lb, int *nr, int *nt, int *nu,
int *itc, int *ist, double *stv, double *alen,
const double *tol);
static double f4xact(int nrow, int *irow, int ncol, int *icol, double dspt,
double *fact, int *icstk, int *ncstk,
int *lstk, int *mstk, int *nstk, int *nrstk, int *irstk,
double *ystk, const double *tol);
static void f5xact(double *pastp, const double *tol, int *kval, int *key,
int *ldkey, int *ipoin, double *stp, int *ldstp,
int *ifrq, int *npoin, int *nr, int *nl, int *ifreq,
int *itop, Rboolean psh);
static Rboolean f6xact(int nrow, int *irow, int *kyy,
int *key, int *ldkey, int *last, int *ipn);
static void f7xact(int nrow, int *imax, int *idif, int *k, int *ks,
int *iflag);
static void f8xact(int *irow, int is, int i1, int izero, int *new);
static double f9xact(int n, int ntot, int *ir, double *fact);
static Rboolean f10act(int nrow, int *irow, int ncol, int *icol, double *val,
double *fact, int *nd, int *ne, int *m);
static void f11act(int *irow, int i1, int i2, int *new);
static int iwork(int iwkmax, int *iwkpt, int number, int itype);
static void isort(int *n, int *ix);
static double gammds(double *y, double *p, int *ifault);
threadlocal bool has_error;
void prterr(int icode, const char *mes) {
has_error++;
Apop_notify(1, "FEXACT error %d.\n%s", icode, mes);
}
/* The interface to the original code, which apop_test_fisher_exact calls: */
static void fexact(int *nrow, int *ncol, int *table, int *ldtabl,
double *expect, double *percnt, double *emin, double *prt,
double *pre, /* new in C : */ int *workspace,
/* new arg, was const = 30*/int *mult) {
/*
ALGORITHM 643, COLLECTED ALGORITHMS FROM ACM.
THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
VOL. 19, NO. 4, DECEMBER, 1993, PP. 484-488.
-----------------------------------------------------------------------
Name: FEXACT
Purpose: Computes Fisher's exact test probabilities and a hybrid
approximation to Fisher exact test probabilities for a
contingency table using the network algorithm.
Arguments:
NROW - The number of rows in the table. (Input)
NCOL - The number of columns in the table. (Input)
TABLE - NROW by NCOL matrix containing the contingency
table. (Input)
LDTABL - Leading dimension of TABLE exactly as specified
in the dimension statement in the calling
program. (Input)
EXPECT - Expected value used in the hybrid algorithm for
deciding when to use asymptotic theory
probabilities. (Input)
If EXPECT <= 0.0 then asymptotic theory probabilities
are not used and Fisher exact test probabilities are
computed. Otherwise, if PERCNT or more of the cells in
the remaining table have estimated expected values of
EXPECT or more, with no remaining cell having expected
value less than EMIN, then asymptotic chi-squared
probabilities are used. See the algorithm section of the
manual document for details.
Use EXPECT = 5.0 to obtain the 'Cochran' condition.
PERCNT - Percentage of remaining cells that must have
estimated expected values greater than EXPECT
before asymptotic probabilities can be used. (Input)
See argument EXPECT for details.
Use PERCNT = 80.0 to obtain the 'Cochran' condition.
EMIN - Minimum cell estimated expected value allowed for
asymptotic chi-squared probabilities to be used. (Input)
See argument EXPECT for details.
Use EMIN = 1.0 to obtain the 'Cochran' condition.
PRT - Probability of the observed table for fixed
marginal totals. (Output)
PRE - Table p-value. (Output)
PRE is the probability of a more extreme table,
where `extreme' is in a probabilistic sense.
If EXPECT < 0 then the Fisher exact probability
is returned. Otherwise, an approximation to the
Fisher exact probability is computed based upon
asymptotic chi-squared probabilities for ``large''
table expected values. The user defines ``large''
through the arguments EXPECT, PERCNT, and EMIN.
Remarks:
1. For many problems one megabyte or more of workspace can be
required. If the environment supports it, the user should begin
by increasing the workspace used to 200,000 units.
2. In FEXACT, LDSTP = MULT*LDKEY. The proportion of table space used
by STP may be changed by changing the line MULT = 30 below to
another value. --> MULT is now an __argument__ of the function
3. FEXACT may be converted to single precision by setting IREAL = 3,
and converting all DOUBLE PRECISION specifications (except the
specifications for RWRK, IWRK, and DWRK) to REAL. This will
require changing the names and specifications of the intrinsic
functions ALOG, AMAX1, AMIN1, EXP, and REAL. In addition, the
machine specific constants will need to be changed, and the name
DWRK will need to be changed to RWRK in the call to F2XACT.
4. Machine specific constants are specified and documented in F2XACT.
A missing value code is specified in both FEXACT and F2XACT.
5. Although not a restriction, is is not generally practical to call
this routine with large tables which are not sparse and in
which the 'hybrid' algorithm has little effect. For example,
although it is feasible to compute exact probabilities for the
table
1 8 5 4 4 2 2
5 3 3 4 3 1 0
10 1 4 0 0 0 0,
computing exact probabilities for a similar table which has been
enlarged by the addition of an extra row (or column) may not be
feasible.
-----------------------------------------------------------------------
*/
/* To increase the length of the table of past path lengths relative
to the length of the hash table, increase MULT.
*/
/* AMISS is a missing value indicator which is returned when the
probability is not defined.
*/
const double amiss = GSL_NAN;
/*
Set IREAL = 4 for DOUBLE PRECISION
Set IREAL = 3 for SINGLE PRECISION
*/
#define i_real 4
#define i_int 2
/* System generated locals */
int ikh;
/* Local variables */
int nco, nro, ntot, numb, iiwk, irwk;
int i, j, k, kk, ldkey, ldstp, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10;
int i3a, i3b, i3c, i9a, iwkmax, iwkpt;
/* Workspace Allocation */
double *equiv;
iwkmax = 2 * (int) (*workspace / 2);
equiv = (double *) calloc(iwkmax / 2, sizeof(double));
#define dwrk (equiv)
#define iwrk ((int *)equiv)
#define rwrk ((float *)equiv)
iwkpt = 0;
Apop_stopif(*nrow > *ldtabl, has_error=true; return, 0, "NROW must be less than or equal to LDTABL.");
ntot = 0;
for (i = 0; i < *nrow; ++i) {
for (j = 0; j < *ncol; ++j) {
if (table[i + j * *ldtabl] < 0)
prterr(2, "All elements of TABLE may not be negative.");
ntot += table[i + j * *ldtabl];
}
}
if (ntot == 0) {
prterr(3, "All elements of TABLE are zero.\n"
"PRT and PRE are set to missing values.");
*pre = *prt = amiss;
free(equiv);
return;
}
/* nco := max(*nrow, *ncol)
* nro := min(*nrow, *ncol) */
if(*ncol > *nrow) {
nco = *ncol;
nro = *nrow;
} else {
nco = *nrow;
nro = *ncol;
}
k = *nrow + *ncol + 1;
kk = k * nco;
ikh = ntot + 1;
i1 = iwork(iwkmax, &iwkpt, ikh, i_real);
i2 = iwork(iwkmax, &iwkpt, nco, i_int);
i3 = iwork(iwkmax, &iwkpt, nco, i_int);
i3a = iwork(iwkmax, &iwkpt, nco, i_int);
i3b = iwork(iwkmax, &iwkpt, nro, i_int);
i3c = iwork(iwkmax, &iwkpt, nro, i_int);
ikh = imax2(k * 5 + (kk << 1), nco * 7 + 800);
iiwk= iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = imax2(nco + 401, k);
irwk= iwork(iwkmax, &iwkpt, ikh, i_real);
/* NOTE:
What follows below splits the remaining amount iwkmax - iwkpt of
(int) workspace into hash tables as follows.
type size index
INT 2 * ldkey i4 i5 i11
REAL 2 * ldkey i8 i9 i10
REAL 2 * ldstp i6
INT 6 * ldstp i7
Hence, we need ldkey times
3 * 2 + 3 * 2 * s + 2 * mult * s + 6 * mult
chunks of integer memory, where s = sizeof(REAL) / sizeof(INT).
If doubles are used and are twice as long as ints, this gives
18 + 10 * mult
so that the value of ldkey can be obtained by dividing available
(int) workspace by this number.
In fact, because iwork() can actually s * n + s - 1 int chunks
when allocating a REAL, we use ldkey = available / numb - 1.
FIXME:
Can we always assume that sizeof(double) / sizeof(int) is 2?
*/
if (i_real == 4) /* Double precision reals */
numb = 18 + 10 * *mult;
else /* Single precision reals */
numb = (*mult << 3) + 12;
ldkey = (iwkmax - iwkpt) / numb - 1;
ldstp = *mult * ldkey;
ikh = ldkey << 1; i4 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldkey << 1; i5 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldstp << 1; i6 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldstp * 6; i7 = iwork(iwkmax, &iwkpt, ikh, i_int);
ikh = ldkey << 1; i8 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1; i9 = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1; i9a = iwork(iwkmax, &iwkpt, ikh, i_real);
ikh = ldkey << 1; i10 = iwork(iwkmax, &iwkpt, ikh, i_int);
/* To convert to double precision, change RWRK to DWRK in the next CALL.
*/
f2xact(*nrow,
*ncol,
table,
*ldtabl,
expect,
percnt,
emin,
prt,
pre,
dwrk + i1,
iwrk + i2,
iwrk + i3,
iwrk + i3a,
iwrk + i3b,
iwrk + i3c,
iwrk + i4,
&ldkey,
iwrk + i5,
dwrk + i6,
&ldstp,
iwrk + i7,
dwrk + i8,
dwrk + i9,
dwrk + i9a,
iwrk + i10,
iwrk + iiwk,
dwrk + irwk);
free(equiv);
}
#undef rwrk
#undef iwrk
#undef dwrk
static void f2xact(int nrow, int ncol, int *table, int ldtabl,
double *expect, double *percnt, double *emin, double *prt,
double *pre, double *fact, int *ico, int *iro, int *kyy,
int *idif, int *irn, int *key, int *ldkey, int *ipoin,
double *stp, int *ldstp, int *ifrq, double *LP, double *SP,
double *tm, int *key2, int *iwk, double *rwk) {
/* -----------------------------------------------------------------------
Name: F2XACT
Purpose: Computes Fisher's exact test for a contingency table,
routine with workspace variables specified.
-----------------------------------------------------------------------
*/
const int imax = INT_MAX;/* the largest representable int on the machine.*/
/* AMISS is a missing value indicator which is returned when the
probability is not defined. */
const double amiss = GSL_NAN;
/* TOL is chosen as the square root of the smallest relative spacing. */
const static double tol = 3.45254e-7;
const char* ch_err_5 =
"The hash table key cannot be computed because the largest key\n"
"is larger than the largest representable int.\n"
"The algorithm cannot proceed.\n"
"Reduce the workspace size or use another algorithm.";
/* Local variables -- changed from "static"
* (*does* change results very slightly on i386 linux) */
int i, ii, j, k, n,
iflag,ifreq, ikkey, ikstp, ikstp2, ipn, ipo, itop, itp = 0,
jkey, jstp, jstp2, jstp3, jstp4, k1, kb, kd, ks, kval = 0, kmax, last,
ncell, ntot, nco, nro, nro2, nrb,
i31, i32, i33, i34, i35, i36, i37, i38, i39,
i41, i42, i43, i44, i45, i46, i47, i48, i310, i311;
double dspt, d1,dd,df,ddf, drn,dro, obs, obs2, obs3, pastp,pv, tmp=0.;
#ifndef USING_R
double d2;
int ifault;
#endif
Rboolean nr_gt_nc, maybe_chisq, chisq = FALSE/* -Wall */, psh;
/* Parameter adjustments */
table -= ldtabl + 1;
--ico;
--iro;
--kyy;
--idif;
--irn;
--key;
--ipoin;
--stp;
--ifrq;
--LP;
--SP;
--tm;
--key2;
--iwk;
--rwk;
/* Check table dimensions */
Apop_stopif(nrow > ldtabl, has_error=true; return, 0, "NROW must be less than or equal to LDTABL.");
Apop_stopif(ncol <= 1, has_error=true; return, 0, "NCOL must be at least 2");
/* Initialize KEY array */
for (i = 1; i <= *ldkey << 1; ++i) {
key[i] = -9999;
key2[i] = -9999;
}
nr_gt_nc = nrow > ncol;
/* nco := max(nrow, ncol) : */
if (nr_gt_nc) nco = nrow;
else nco = ncol;
/* Compute row marginals and total */
ntot = 0;
for (i = 1; i <= nrow; ++i) {
iro[i] = 0;
for (j = 1; j <= ncol; ++j) {
Apop_stopif(table[i + j * ldtabl] < 0., has_error=true; return,
0, "All elements of TABLE must be non-negative.");
iro[i] += table[i + j * ldtabl];
}
ntot += iro[i];
}
if (ntot == 0) {
prterr(3, "All elements of TABLE are zero.\n"
"PRT and PRE are set to missing values.");
*pre = *prt = amiss;
return;
}
/* Column marginals */
for (i = 1; i <= ncol; ++i) {
ico[i] = 0;
for (j = 1; j <= nrow; ++j)
ico[i] += table[j + i * ldtabl];
}
/* sort marginals */
isort(&nrow, &iro[1]);
isort(&ncol, &ico[1]);
/* Determine row and column marginals.
Define max(nrow,ncol) =: nco >= nro := min(nrow,ncol)
nco is defined above
Swap marginals if necessary to ico[1:nco] & iro[1:nro]
*/
if (nr_gt_nc) {
nro = ncol;
/* Swap marginals */
for (i = 1; i <= nco; ++i) {
ii = iro[i];
if (i <= nro) iro[i] = ico[i];
ico[i] = ii;
}
} else
nro = nrow;
/* Get multiplers for stack */
kyy[1] = 1;
for (i = 1; i < nro; ++i) {
/* Hash table multipliers */
if (iro[i] + 1 <= imax / kyy[i]) {
kyy[i + 1] = kyy[i] * (iro[i] + 1);
j /= kyy[i];
}
else {
prterr(5, ch_err_5);
return;
}
}
/* Check for Maximum product : */
/* original code: if (iro[nro - 1] + 1 > imax / kyy[nro - 1]) */
if (iro[nro] + 1 > imax / kyy[nro]) {
prterr(501, ch_err_5);
return;
}
/* Compute log factorials */
fact[0] = 0.;
fact[1] = 0.;
if(ntot >= 2) fact[2] = log(2.);
/* MM: old code assuming log() to be SLOW */
for (i = 3; i <= ntot; i += 2) {
fact[i] = fact[i - 1] + log((double) i);
j = i + 1;
if (j <= ntot)
fact[j] = fact[i] + fact[2] + fact[j / 2] - fact[j / 2 - 1];
}
/* Compute obs := observed path length */
obs = tol;
ntot = 0;
for (j = 1; j <= nco; ++j) {
dd = 0.;
if (nr_gt_nc) {
for (i = 1; i <= nro; ++i) {
dd += fact[table[j + i * ldtabl]];
ntot += table[j + i * ldtabl];
}
} else {
for (i = 1, ii = j * ldtabl + 1; i <= nro; i++, ii++) {
dd += fact[table[ii]];
ntot += table[ii];
}
}
obs += fact[ico[j]] - dd;
}
/* Denominator of observed table: DRO */
dro = f9xact(nro, ntot, &iro[1], fact);
/* improve: the following "easily" underflows to zero -- return "log()" */
*prt = exp(obs - dro);
*pre = 0.;
itop = 0;
maybe_chisq = (*expect > 0.);
/* Initialize pointers for workspace */
/* f3xact */
i31 = 1;
i32 = i31 + nco;
i33 = i32 + nco;
i34 = i33 + nco;
i35 = i34 + nco;
i36 = i35 + nco;
i37 = i36 + nco;
i38 = i37 + nco;
i39 = i38 + 400;
i310 = 1;
i311 = 1 + 400;
/* f4xact */
i = nrow + ncol + 1;
i41 = 1;
i42 = i41 + i;
i43 = i42 + i;
i44 = i43 + i;
i45 = i44 + i;
i46 = i45 + i;
i47 = i46 + i * nco;
i48 = 1;
/* Initialize pointers */
k = nco;
last = *ldkey + 1;
jkey = *ldkey + 1;
jstp = *ldstp + 1;
jstp2 = *ldstp * 3 + 1;
jstp3 = (*ldstp << 2) + 1;
jstp4 = *ldstp * 5 + 1;
ikkey = 0;
ikstp = 0;
ikstp2 = *ldstp << 1;
ipo = 1;
ipoin[1] = 1;
stp[1] = 0.;
ifrq[1] = 1;
ifrq[ikstp2 + 1] = -1;
Outer_Loop:
kb = nco - k + 1;
ks = 0;
n = ico[kb];
kd = nro + 1;
kmax = nro;
/* IDIF is the difference in going to the daughter */
for (i = 1; i <= nro; ++i)
idif[i] = 0;
/* Generate the first daughter */
do {
--kd;
ntot = imin2(n, iro[kd]);
idif[kd] = ntot;
if (idif[kmax] == 0)
--kmax;
n -= ntot;
} while (n > 0 && kd != 1);
if (n != 0) /* i.e. kd == 1 */
goto L310;
k1 = k - 1;
n = ico[kb];
ntot = 0;
for (i = kb + 1; i <= nco; ++i)
ntot += ico[i];
L150:
/* Arc to daughter length=ICO[KB] */
for (i = 1; i <= nro; ++i)
irn[i] = iro[i] - idif[i];
if (k1 > 1) {
/* Sort irn */
if (nro == 2) {
if (irn[1] > irn[2]) {
ii = irn[1]; irn[1] = irn[2]; irn[2] = ii;
}
} else
isort(&nro, &irn[1]);
/* Adjust start for zero */
for (i = 1; i <= nro; ++i) {
if (irn[i] != 0)
break;
}
nrb = i;
} else
nrb = 1;
nro2 = nro - nrb + 1;
/* Some table values */
ddf = f9xact(nro, n, &idif[1], fact);
drn = f9xact(nro2, ntot, &irn[nrb], fact) - dro + ddf;
/* Get hash value */
if (k1 > 1) {
kval = irn[1];
/* Note that with the corrected check at error "502",
* we won't have overflow in kval below : */
for (i = 2; i <= nro; ++i)
kval += irn[i] * kyy[i];
/* Get hash table entry */
i = kval % (*ldkey << 1) + 1;
/* Search for unused location */
for (itp = i; itp <= *ldkey << 1; ++itp) {
ii = key2[itp];
if (ii == kval) {
goto L240;
} else if (ii < 0) {
key2[itp] = kval;
LP[itp] = 1.;
SP[itp] = 1.;
goto L240;
}
}
for (itp = 1; itp <= i - 1; ++itp) {
ii = key2[itp];
if (ii == kval)
goto L240;
else if (ii < 0) {
key2[itp] = kval;
LP[itp] = 1.;
goto L240;
}
}
/* KH
prterr(6, "LDKEY is too small.\n"
"It is not possible to give the value of LDKEY required,\n"
"but you could try doubling LDKEY (and possibly LDSTP).");
*/
prterr(6, "LDKEY is too small for this problem.\n"
"Try increasing the size of the workspace.");
}
L240:
psh = TRUE;
/* Recover pastp */
ipn = ipoin[ipo + ikkey];
pastp = stp[ipn + ikstp];
ifreq = ifrq[ipn + ikstp];
/* Compute shortest and longest path */
if (k1 > 1) {
obs2 = obs - fact[ico[kb + 1]] - fact[ico[kb + 2]] - ddf;
for (i = 3; i <= k1; ++i)
obs2 -= fact[ico[kb + i]];
if (LP[itp] > 0.) {
dspt = obs - obs2 - ddf;
/* Compute longest path */
LP[itp] = f3xact(nro2, &irn[nrb], k1, &ico[kb + 1], ntot, fact,
&iwk[i31], &iwk[i32], &iwk[i33], &iwk[i34],
&iwk[i35], &iwk[i36], &iwk[i37], &iwk[i38],
&iwk[i39], &rwk[i310], &rwk[i311], &tol);
if(LP[itp] > 0.) {/* can this happen? */
printf("___ LP[itp=%d] = %g > 0\n", itp, LP[itp]);
LP[itp] = 0.;
}
/* Compute shortest path -- using dspt as offset */
SP[itp] = f4xact(nro2, &irn[nrb], k1, &ico[kb + 1], dspt, fact,
&iwk[i47], &iwk[i41], &iwk[i42], &iwk[i43],
&iwk[i44], &iwk[i45], &iwk[i46], &rwk[i48], &tol);
/* SP[itp] = fmin2(0., SP[itp] - dspt);*/
if(SP[itp] > 0.) { /* can this happen? */
printf("___ SP[itp=%d] = %g > 0\n", itp, SP[itp]);
SP[itp] = 0.;
}
/* Use chi-squared approximation? */
if (maybe_chisq && (irn[nrb] * ico[kb + 1]) > ntot * *emin) {
ncell = 0.;
for (i = 0; i < nro2; ++i)
for (j = 1; j <= k1; ++j)
if (irn[nrb + i] * ico[kb + j] >= ntot * *expect)
ncell++;
if (ncell * 100 >= k1 * nro2 * *percnt) {
tmp = 0.;
for (i = 0; i < nro2; ++i)
tmp += (fact[irn[nrb + i]] -
fact[irn[nrb + i] - 1]);
tmp *= k1 - 1;
for (j = 1; j <= k1; ++j)
tmp += (nro2 - 1) * (fact[ico[kb + j]] -
fact[ico[kb + j] - 1]);
df = (double) ((nro2 - 1) * (k1 - 1));
tmp += df * 1.83787706640934548356065947281;
tmp -= (nro2 * k1 - 1) * (fact[ntot] - fact[ntot - 1]);
tm[itp] = (obs - dro) * -2. - tmp;
} else {
/* tm[itp] set to a flag value */
tm[itp] = -9876.;
}
} else
tm[itp] = -9876.;
}
obs3 = obs2 - LP[itp];
obs2 -= SP[itp];
if (tm[itp] == -9876.)
chisq = FALSE;
else {
chisq = TRUE;
tmp = tm[itp];
}
} else {
obs2 = obs - drn - dro;
obs3 = obs2;
}
L300:
/* Process node with new PASTP */
if (pastp <= obs3) /* Update pre */
*pre += (double) ifreq * exp(pastp + drn);
else if (pastp < obs2) {
if (chisq) {
df = (double) ((nro2 - 1) * (k1 - 1));
d1 = fmax2(0., tmp + (pastp + drn) * 2.) / 2.;
d2 = df / 2.;
pv = 1. - gammds(&d1, &d2, &ifault);
*pre += (double) ifreq * exp(pastp + drn) * pv;
} else {
/* Put daughter on queue */
d1 = pastp + ddf;
f5xact(&d1, &tol, &kval, &key[jkey], ldkey, &ipoin[jkey],
&stp[jstp], ldstp, &ifrq[jstp], &ifrq[jstp2],
&ifrq[jstp3], &ifrq[jstp4], &ifreq, &itop, psh);
psh = FALSE;
}
}
/* Get next PASTP on chain */
ipn = ifrq[ipn + ikstp2];
if (ipn > 0) {
pastp = stp[ipn + ikstp];
ifreq = ifrq[ipn + ikstp];
goto L300;
}
/* Generate a new daughter node */
f7xact(kmax, &iro[1], &idif[1], &kd, &ks, &iflag);
if (iflag != 1)
goto L150;
L310:
/* Go get a new mother from stage K */
do {
if(!f6xact(nro, &iro[1], &kyy[1], &key[ikkey + 1], ldkey, &last, &ipo))
/* Update pointers */
goto Outer_Loop;
/* else : no additional nodes to process */
--k;
itop = 0;
ikkey = jkey - 1;
ikstp = jstp - 1;
ikstp2 = jstp2 - 1;
jkey = *ldkey - jkey + 2;
jstp = *ldstp - jstp + 2;
jstp2 = (*ldstp << 1) + jstp;
for (i = 1; i <= *ldkey << 1; ++i)
key2[i] = -9999;
} while (k >= 2);
}/* f2xact() */
static double f3xact(int nrow, int *irow, int ncol, int *icol,
int ntot, double *fact, int *ico, int *iro, int *it,
int *lb, int *nr, int *nt, int *nu, int *itc, int *ist,
double *stv, double *alen, const double *tol) {
/* -----------------------------------------------------------------------
Name: F3XACT
Purpose: Computes the longest path length for a given table.
Arguments:
NROW - The number of rows in the table. (Input)
IROW - Vector of length NROW containing the row sums
for the table. (Input)
NCOL - The number of columns in the table. (Input)
ICOL - Vector of length K containing the column sums
for the table. (Input)
NTOT - The total count in the table. (Input)
FACT - Vector containing the logarithms of factorials. (Input)
ICO - Work vector of length MAX(NROW,NCOL).
IRO - Work vector of length MAX(NROW,NCOL).
IT - Work vector of length MAX(NROW,NCOL).
LB - Work vector of length MAX(NROW,NCOL).
NR - Work vector of length MAX(NROW,NCOL).
NT - Work vector of length MAX(NROW,NCOL).
NU - Work vector of length MAX(NROW,NCOL).
ITC - Work vector of length 400.
IST - Work vector of length 400.
STV - Work vector of length 400.
ALEN - Work vector of length MAX(NROW,NCOL).
TOL - Tolerance. (Input)
Return Value :
LP - The longest path for the table. (Output)
-----------------------------------------------------------------------
*/
const int ldst = 200;/* half stack size */
/* Initialized data */
static int nst = 0;
static int nitc = 0;
int i, k;
int n11, n12, ii, nn, ks, ic1, ic2, nc1, nn1;
int nr1, nco, nct, ipn, irl, key, lev, itp, nro, nrt, kyy, nc1s;
double LP, v, val, vmn;
Rboolean xmin;
--stv;
--ist;
--itc;
--nu;
--nt;
--nr;
--lb;
--it;
--iro;
--ico;
--icol;
--irow;
if (nrow <= 1) { /* nrow is 1 */
LP = 0.;
if (nrow > 0)
for (i = 1; i <= ncol; ++i)
LP -= fact[icol[i]];
return LP;
}
if (ncol <= 1) { /* ncol is 1 */
LP = 0.;
if (ncol > 0) {
for (i = 1; i <= nrow; ++i)
LP -= fact[irow[i]];
}
return LP;
}
/* 2 by 2 table */
if (nrow * ncol == 4) {
n11 = (irow[1] + 1) * (icol[1] + 1) / (ntot + 2);
n12 = irow[1] - n11;
return -(fact[n11] + fact[n12] +
fact[icol[1] - n11] + fact[icol[2] - n12]);
}
/* ELSE: larger than 2 x 2 : */
/* Test for optimal table */
val = 0.;
if (irow[nrow] <= irow[1] + ncol)
xmin = f10act(nrow, &irow[1], ncol, &icol[1], &val, fact,
&lb[1], &nu[1], &nr[1]);
else xmin = FALSE;
if (! xmin && icol[ncol] <= icol[1] + nrow)
xmin = f10act(ncol, &icol[1], nrow, &irow[1], &val, fact,
&lb[1], &nu[1], &nr[1]);
if (xmin)
return - val;
/* Setup for dynamic programming */
for (i = 0; i <= ncol; ++i)
alen[i] = 0.;
for (i = 1; i <= 2*ldst; ++i)
ist[i] = -1;
nn = ntot;
/* Minimize ncol */
if (nrow >= ncol) {
nro = nrow;
nco = ncol;
ico[1] = icol[1];
nt[1] = nn - ico[1];
for (i = 2; i <= ncol; ++i) {
ico[i] = icol[i];
nt[i] = nt[i - 1] - ico[i];
}
for (i = 1; i <= nrow; ++i)
iro[i] = irow[i];
} else {
nro = ncol;
nco = nrow;
ico[1] = irow[1];
nt[1] = nn - ico[1];
for (i = 2; i <= nrow; ++i) {
ico[i] = irow[i];
nt[i] = nt[i - 1] - ico[i];
}
for (i = 1; i <= ncol; ++i)
iro[i] = icol[i];
}
nc1s = nco - 1;
kyy = ico[nco] + 1;
/* Initialize pointers */
vmn = 1e100;/* to contain min(v..) */
irl = 1;
ks = 0;
k = ldst;
LnewNode: /* Setup to generate new node */
lev = 1;
nr1 = nro - 1;
nrt = iro[irl];
nct = ico[1];
lb[1] = (int) ((((double) nrt + 1) * (nct + 1)) /
(double) (nn + nr1 * nc1s + 1) - *tol) - 1;
nu[1] = (int) ((((double) nrt + nc1s) * (nct + nr1)) /
(double) (nn + nr1 + nc1s)) - lb[1] + 1;
nr[1] = nrt - lb[1];
LoopNode: /* Generate a node */
--nu[lev];
if (nu[lev] == 0) {
if (lev == 1)
goto L200;
--lev;
goto LoopNode;
}
++lb[lev];
--nr[lev];
while(1) {
alen[lev] = alen[lev - 1] + fact[lb[lev]];
if (lev >= nc1s)
break;
nn1 = nt[lev];
nrt = nr[lev];
++lev;
nc1 = nco - lev;
nct = ico[lev];
lb[lev] = (int) ((((double) nrt + 1) * (nct + 1)) /
(double) (nn1 + nr1 * nc1 + 1) - *tol);
nu[lev] = (int) ((((double) nrt + nc1) * (nct + nr1)) /
(double) (nn1 + nr1 + nc1) - lb[lev] + 1);
nr[lev] = nrt - lb[lev];
}
alen[nco] = alen[lev] + fact[nr[lev]];
lb[nco] = nr[lev];
v = val + alen[nco];
if (nro == 2) { /* Only 1 row left */
v += fact[ico[1] - lb[1]] + fact[ico[2] - lb[2]];
for (i = 3; i <= nco; ++i)
v += fact[ico[i] - lb[i]];
if (v < vmn)
vmn = v;
} else if (nro == 3 && nco == 2) { /* 3 rows and 2 columns */
nn1 = nn - iro[irl] + 2;
ic1 = ico[1] - lb[1];
ic2 = ico[2] - lb[2];
n11 = (iro[irl + 1] + 1) * (ic1 + 1) / nn1;
n12 = iro[irl + 1] - n11;
v += fact[n11] + fact[n12] + fact[ic1 - n11] + fact[ic2 - n12];
if (v < vmn)
vmn = v;
} else { /* Column marginals are new node */
for (i = 1; i <= nco; ++i)
it[i] = imax2(ico[i] - lb[i], 0);
/* Sort column marginals it[] : */
if (nco == 2) {
if (it[1] > it[2]) { /* swap */
ii = it[1]; it[1] = it[2]; it[2] = ii;
}
} else
isort(&nco, &it[1]);
/* Compute hash value */
key = it[1] * kyy + it[2];
for (i = 3; i <= nco; ++i) {
key = it[i] + key * kyy;
}
if (key < -1){
if (apop_opts.verbose)
printf("Bug in FEXACT: gave negative key.\n");
return -1;
}
/* Table index */
ipn = key % ldst + 1;
/* Find empty position */
for (itp = ipn, ii = ks + ipn; itp <= ldst; ++itp, ++ii) {
if (ist[ii] < 0) {
goto L180;
} else if (ist[ii] == key) {
goto L190;
}
}
for (itp = 1, ii = ks + 1; itp <= ipn - 1; ++itp, ++ii) {
if (ist[ii] < 0) {
goto L180;
} else if (ist[ii] == key) {
goto L190;
}